#include <itkAffineDTI3DTransform.h>

Detailed Description

template<class TScalarType = double>
class itk::AffineDTI3DTransform< TScalarType >

AffineDTI3DTransform of a vector space (e.g. space coordinates)

This transform applies an affine transformation, but is parameterized by angles, shear factors, scales, and translation, instead of by the affine matrix. It is meant for registration of MR diffusion weighted images, but could be used for other images as well of course.

The affine model is adopted from the following paper: [1] A. Leemans and D.K. Jones. "The B-matrix must be rotated when correcting for subject motion in DTI data". Magnetic Resonance in Medicine, Volume 61, Issue 6, pages 1336 - 1349, 2009.

The model is as follows:
T(x) = R G S (x-c) + t + c
with:

R = Rx Ry Rz (rotation matrices)
G = Gx Gy Gz (shear matrices)
S = diag( [sx sy sz] ) (scaling matrix)
c = center of rotation
t = translation See [1] for exact expressions for Rx, Gx etc.

Using this model, the rotation components can be easily extracted an applied to the B-matrix.

The parameters are ordered as follows: in 2D: [ Angle ShearX ShearY ScaleX ScaleY TranslationX TranslationY ] in 3D: [ AngleX AngleY AngleZ ShearX ShearY ShearZ ScaleX ScaleY ScaleZ TranslationX TranslationY TranslationZ ]

The serialization of the fixed parameters is an array of 2 elements defining the center of rotation.

This transform applies an affine transformation, but is parameterized by angles, shear factors, scales, and translation, instead of by the affine matrix. It is meant for registration of MR diffusion weighted images, but could be used for other images as well of course.

The affine model is adopted from the following paper: [1] A. Leemans and D.K. Jones. "The B-matrix must be rotated when correcting for subject motion in DTI data". Magnetic Resonance in Medicine, Volume 61, Issue 6, pages 1336 - 1349, 2009.

The model is as follows:
T(x) = R G S (x-c) + t + c
with:

R = Rx Ry Rz (rotation matrices)
G = Gx Gy Gz (shear matrices)
S = diag( [sx sy sz] ) (scaling matrix)
c = center of rotation
t = translation See [1] for exact expressions for Rx, Gx etc.

Using this model, the rotation components can be easily extracted an applied to the B-matrix.

The parameters are ordered as follows: [ AngleX AngleY AngleZ ShearX ShearY ShearZ ScaleX ScaleY ScaleZ TranslationX TranslationY TranslationZ ]

The serialization of the fixed parameters is an array of 3 elements defining the center of rotation.

Definition at line 78 of file itkAffineDTI3DTransform.h.

Inheritance diagram for itk::AffineDTI3DTransform< TScalarType >:

[legend]

Public Types
using	AngleType = typename Superclass::ScalarType

using	CenterType = InputPointType

using	ConstPointer = SmartPointer< const Self >

using	InverseMatrixType = Matrix< TScalarType, Self::InputSpaceDimension, Self::OutputSpaceDimension >

using	MatrixType = Matrix< TScalarType, Self::OutputSpaceDimension, Self::InputSpaceDimension >

using	OffsetType = OutputVectorType

using	Pointer = SmartPointer< Self >

using	ScalarArrayType = FixedArray< ScalarType >

using	Self = AffineDTI3DTransform

using	Superclass = AdvancedMatrixOffsetTransformBase< TScalarType, 3, 3 >

using	TranslationType = OutputVectorType

Public Types inherited from itk::AdvancedMatrixOffsetTransformBase< TScalarType, NInputDimensions, NOutputDimensions >
using	CenterType = InputPointType

using	ConstPointer = SmartPointer< const Self >

using	InverseMatrixType = Matrix< TScalarType, Self::InputSpaceDimension, Self::OutputSpaceDimension >

using	MatrixType = Matrix< TScalarType, Self::OutputSpaceDimension, Self::InputSpaceDimension >

using	OffsetType = OutputVectorType

using	Pointer = SmartPointer< Self >

using	Self = AdvancedMatrixOffsetTransformBase

using	Superclass = AdvancedTransform< TScalarType, NInputDimensions, NOutputDimensions >

using	TranslationType = OutputVectorType

Public Types inherited from itk::AdvancedTransform< TScalarType, NInputDimensions, NOutputDimensions >
using	ConstPointer = SmartPointer< const Self >

using	InternalMatrixType = typename SpatialJacobianType::InternalMatrixType

using	InverseTransformBaseType = typename Superclass::InverseTransformBaseType

using	JacobianOfSpatialHessianType = std::vector< SpatialHessianType >

using	JacobianOfSpatialJacobianType = std::vector< SpatialJacobianType >

using	MovingImageGradientType = OutputCovariantVectorType

using	MovingImageGradientValueType = typename MovingImageGradientType::ValueType

using	NonZeroJacobianIndicesType = std::vector< unsigned long >

using	Pointer = SmartPointer< Self >

using	Self = AdvancedTransform

using	SpatialHessianType = FixedArray< Matrix< ScalarType, InputSpaceDimension, InputSpaceDimension >, OutputSpaceDimension >

using	SpatialJacobianType = Matrix< ScalarType, OutputSpaceDimension, InputSpaceDimension >

using	Superclass = Transform< TScalarType, NInputDimensions, NOutputDimensions >

using	TransformType = Transform< TScalarType, NInputDimensions, NOutputDimensions >

using	TransformTypeConstPointer = typename TransformType::ConstPointer

using	TransformTypePointer = typename TransformType::Pointer

Public Member Functions
virtual const char *	GetClassName () const

void	GetJacobian (const InputPointType &, JacobianType &, NonZeroJacobianIndicesType &) const override

const ParametersType &	GetParameters () const override

	ITK_DISALLOW_COPY_AND_MOVE (AffineDTI3DTransform)

	itkStaticConstMacro (InputSpaceDimension, unsigned int, 3)

	itkStaticConstMacro (OutputSpaceDimension, unsigned int, 3)

	itkStaticConstMacro (ParametersDimension, unsigned int, 12)

	itkStaticConstMacro (SpaceDimension, unsigned int, 3)

void	SetIdentity () override

void	SetParameters (const ParametersType &parameters) override

Public Member Functions inherited from itk::AdvancedMatrixOffsetTransformBase< TScalarType, NInputDimensions, NOutputDimensions >
const InputPointType &	GetCenter () const

virtual const char *	GetClassName () const

const FixedParametersType &	GetFixedParameters () const override

void	GetJacobian (const InputPointType &, JacobianType &, NonZeroJacobianIndicesType &) const override

void	GetJacobianOfSpatialHessian (const InputPointType &, JacobianOfSpatialHessianType &, NonZeroJacobianIndicesType &) const override

void	GetJacobianOfSpatialHessian (const InputPointType &inputPoint, SpatialHessianType &sh, JacobianOfSpatialHessianType &jsh, NonZeroJacobianIndicesType &nonZeroJacobianIndices) const override

void	GetJacobianOfSpatialJacobian (const InputPointType &, JacobianOfSpatialJacobianType &, NonZeroJacobianIndicesType &) const override

void	GetJacobianOfSpatialJacobian (const InputPointType &, SpatialJacobianType &, JacobianOfSpatialJacobianType &, NonZeroJacobianIndicesType &) const override

const MatrixType &	GetMatrix () const

const ParametersType &	GetParameters () const override

void	GetSpatialHessian (const InputPointType &, SpatialHessianType &) const override

void	GetSpatialJacobian (const InputPointType &, SpatialJacobianType &) const override

TransformCategoryEnum	GetTransformCategory () const override

const OutputVectorType &	GetTranslation () const

bool	IsLinear () const override

	itkStaticConstMacro (InputSpaceDimension, unsigned int, NInputDimensions)

	itkStaticConstMacro (OutputSpaceDimension, unsigned int, NOutputDimensions)

	itkStaticConstMacro (ParametersDimension, unsigned int, NOutputDimensions *(NInputDimensions+1))

void	SetCenter (const InputPointType &center)

void	SetFixedParameters (const FixedParametersType &) override

virtual void	SetIdentity ()

virtual void	SetMatrix (const MatrixType &matrix)

void	SetParameters (const ParametersType &parameters) override

void	SetTranslation (const OutputVectorType &translation)

OutputCovariantVectorType	TransformCovariantVector (const InputCovariantVectorType &vector) const override

OutputPointType	TransformPoint (const InputPointType &point) const override

OutputVectorType	TransformVector (const InputVectorType &vector) const override

OutputVnlVectorType	TransformVector (const InputVnlVectorType &vector) const override

Public Member Functions inherited from itk::AdvancedTransform< TScalarType, NInputDimensions, NOutputDimensions >
void	ComputeJacobianWithRespectToParameters (const InputPointType &, JacobianType &) const override

virtual void	EvaluateJacobianWithImageGradientProduct (const InputPointType &inputPoint, const MovingImageGradientType &movingImageGradient, DerivativeType &imageJacobian, NonZeroJacobianIndicesType &nonZeroJacobianIndices) const

virtual const char *	GetClassName () const

virtual bool	GetHasNonZeroJacobianOfSpatialHessian () const

virtual bool	GetHasNonZeroSpatialHessian () const

virtual void	GetJacobian (const InputPointType &inputPoint, JacobianType &j, NonZeroJacobianIndicesType &nonZeroJacobianIndices) const =0

virtual void	GetJacobianOfSpatialHessian (const InputPointType &inputPoint, JacobianOfSpatialHessianType &jsh, NonZeroJacobianIndicesType &nonZeroJacobianIndices) const =0

virtual void	GetJacobianOfSpatialHessian (const InputPointType &inputPoint, SpatialHessianType &sh, JacobianOfSpatialHessianType &jsh, NonZeroJacobianIndicesType &nonZeroJacobianIndices) const =0

virtual void	GetJacobianOfSpatialJacobian (const InputPointType &inputPoint, JacobianOfSpatialJacobianType &jsj, NonZeroJacobianIndicesType &nonZeroJacobianIndices) const =0

virtual void	GetJacobianOfSpatialJacobian (const InputPointType &inputPoint, SpatialJacobianType &sj, JacobianOfSpatialJacobianType &jsj, NonZeroJacobianIndicesType &nonZeroJacobianIndices) const =0

virtual NumberOfParametersType	GetNumberOfNonZeroJacobianIndices () const

virtual void	GetSpatialHessian (const InputPointType &inputPoint, SpatialHessianType &sh) const =0

virtual void	GetSpatialJacobian (const InputPointType &inputPoint, SpatialJacobianType &sj) const =0

	ITK_DISALLOW_COPY_AND_MOVE (AdvancedTransform)

	itkStaticConstMacro (InputSpaceDimension, unsigned int, NInputDimensions)

	itkStaticConstMacro (OutputSpaceDimension, unsigned int, NOutputDimensions)

Static Public Member Functions
static Pointer	New ()

Static Public Member Functions inherited from itk::AdvancedMatrixOffsetTransformBase< TScalarType, NInputDimensions, NOutputDimensions >
static Pointer	New ()

Protected Member Functions
	AffineDTI3DTransform ()

	AffineDTI3DTransform (const MatrixType &matrix, const OutputPointType &offset)

	AffineDTI3DTransform (unsigned int outputSpaceDims, unsigned int paramsSpaceDims)

void	ComputeMatrix () override

void	ComputeMatrixParameters () override

virtual void	PrecomputeJacobianOfSpatialJacobian ()

void	PrintSelf (std::ostream &os, Indent indent) const override

void	SetVarAngleScaleShear (ScalarArrayType angle, ScalarArrayType shear, ScalarArrayType scale)

	~AffineDTI3DTransform () override=default

Protected Member Functions inherited from itk::AdvancedMatrixOffsetTransformBase< TScalarType, NInputDimensions, NOutputDimensions >
	AdvancedMatrixOffsetTransformBase (const unsigned int paramDims=ParametersDimension)

virtual void	ComputeMatrix ()

virtual void	ComputeMatrixParameters ()

virtual void	ComputeOffset ()

void	ComputeTranslation ()

const OutputVectorType &	GetOffset () const

void	PrintSelf (std::ostream &s, Indent indent) const override

void	SetVarMatrix (const MatrixType &matrix)

void	SetVarTranslation (const OutputVectorType &translation)

	~AdvancedMatrixOffsetTransformBase () override=default

Protected Member Functions inherited from itk::AdvancedTransform< TScalarType, NInputDimensions, NOutputDimensions >
	AdvancedTransform ()=default

	~AdvancedTransform () override=default

Private Attributes
ScalarArrayType	m_Angle

ScalarArrayType	m_Scale

ScalarArrayType	m_Shear

Additional Inherited Members
Protected Attributes inherited from itk::AdvancedMatrixOffsetTransformBase< TScalarType, NInputDimensions, NOutputDimensions >
JacobianOfSpatialHessianType	m_JacobianOfSpatialHessian

JacobianOfSpatialJacobianType	m_JacobianOfSpatialJacobian

NonZeroJacobianIndicesType	m_NonZeroJacobianIndices

SpatialHessianType	m_SpatialHessian

Protected Attributes inherited from itk::AdvancedTransform< TScalarType, NInputDimensions, NOutputDimensions >
bool	m_HasNonZeroJacobianOfSpatialHessian { true }

bool	m_HasNonZeroSpatialHessian { true }